Periodic Solutions Of Several Kinds Of Difference Equations

This thesis mainly studies the existence of periodic solutions for some difference equations.It is consisted of four chapters.In Chapter 1,the background and history of difference equations are briefly addressed,and the main work of this paper are given.In Chapter 2,we focus on the existence of positive periodic solutions for two class of functional difference equationsx(n+1)=A(n,x(n-τ(n)))x(n)+f(n,x(n-τ(n))),(1)x(n+1)=A(n,x(n-τ(n)))x(n)-f(n,x(n-τ(n))),(2) where A(n,·) andτ(n):Z→Z areω-periodic(ωis positive integer). f:R×[0,+∞)→[0,+∞),A:R×[0,+∞)→[0,+∞) are continuous.Using fixed point theorem in cone,we obtain some sufficient conditions guaranteeing that(1) or(2) has at least one positive periodic solution,which extend some known results.Chapter 3 deals with the existence of positive periodic solution for the following difference equation-△x(n) = f(n + 1,x(n + 1))(3) where△x(n) = x(n + 1) - x(n),f:Z×R are continuous and f areω-periodic in n.By using fixed point theorem in cone,we obtain some existence results for(3). Chapter 4 concems the existence of periodic solution of neutral functional difference equation△(x(n)-g(n,x(n-τ(n)))) = a(n)x(n)-f(n,x(n-τ(n)))(4) where△x(n)=x(n+1)-x(n),τ:Z→Z,g,f:Z×R→R are continuous, a,τand g,f areω-periodic in n.By using Krasnoselskii fixed point theorem,we obtain existence results for(4).